LMFDB - Embedded newform 507.2.p.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.83220 - 0.694863i) q^{2} +(0.568065 + 0.822984i) q^{3} +(1.37712 + 1.22002i) q^{4} +(-0.128032 - 0.0155459i) q^{5} +(-0.468949 - 1.90260i) q^{6} +(-2.04557 - 3.89750i) q^{7} +(0.145878 + 0.277948i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.223779 + 0.117448i) q^{10} +(3.55789 - 1.34933i) q^{11} +(-0.221764 + 1.82639i) q^{12} +(-3.60522 + 0.0489021i) q^{13} +(1.03966 + 8.56241i) q^{14} +(-0.0599366 - 0.114200i) q^{15} +(-0.517672 - 4.26341i) q^{16} +(-2.75654 + 1.44675i) q^{17} +(1.29942 - 1.46674i) q^{18} +4.71334i q^{19} +(-0.157349 - 0.177610i) q^{20} +(2.04557 - 3.89750i) q^{21} -7.45637 q^{22} -0.800231 q^{23} +(-0.145878 + 0.277948i) q^{24} +(-4.83856 - 1.19260i) q^{25} +(6.63948 + 2.41554i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(1.93804 - 7.86294i) q^{28} +(0.257912 - 0.680057i) q^{29} +(0.0304629 + 0.250885i) q^{30} +(-2.01302 - 8.16715i) q^{31} +(-1.86376 + 7.56158i) q^{32} +(3.13158 + 2.16158i) q^{33} +(6.05584 - 0.735312i) q^{34} +(0.201308 + 0.530806i) q^{35} +(-1.62907 + 0.855001i) q^{36} +(-2.53811 - 10.2975i) q^{37} +(3.27513 - 8.63580i) q^{38} +(-2.08824 - 2.93926i) q^{39} +(-0.0143562 - 0.0378541i) q^{40} +(4.40336 - 3.03942i) q^{41} +(-6.45613 + 5.71963i) q^{42} +(-5.17226 - 1.27485i) q^{43} +(6.54582 + 2.48250i) q^{44} +(0.0599366 - 0.114200i) q^{45} +(1.46619 + 0.556051i) q^{46} +(-3.08985 - 3.48772i) q^{47} +(3.21465 - 2.84793i) q^{48} +(-7.02972 + 10.1843i) q^{49} +(8.03654 + 5.54722i) q^{50} +(-2.75654 - 1.44675i) q^{51} +(-5.02447 - 4.33109i) q^{52} +(-11.8834 + 6.23691i) q^{53} +(1.94526 + 0.236197i) q^{54} +(-0.476501 + 0.117447i) q^{55} +(0.784899 - 1.13712i) q^{56} +(-3.87900 + 2.67748i) q^{57} +(-0.945094 + 1.06679i) q^{58} +(-6.37878 - 0.774524i) q^{59} +(0.0567860 - 0.230390i) q^{60} +(-6.29223 - 3.30242i) q^{61} +(-1.98679 + 16.3627i) q^{62} +(4.36959 - 0.530565i) q^{63} +(3.78970 - 5.49033i) q^{64} +(0.462345 + 0.0497854i) q^{65} +(-4.23570 - 6.13647i) q^{66} +(8.80563 + 9.93951i) q^{67} +(-5.56114 - 1.37070i) q^{68} +(-0.454583 - 0.658577i) q^{69} -1.11243i q^{70} +(-3.77565 + 2.60615i) q^{71} +(-0.311615 + 0.0378369i) q^{72} +(-0.0826716 + 0.0313532i) q^{73} +(-2.50503 + 20.6308i) q^{74} +(-1.76713 - 4.65953i) q^{75} +(-5.75036 + 6.49081i) q^{76} +(-12.5369 - 11.1067i) q^{77} +(1.78371 + 6.83637i) q^{78} +(6.96403 - 6.16959i) q^{79} +0.553902i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-10.1798 + 2.50911i) q^{82} +(-2.47482 - 1.70825i) q^{83} +(7.57200 - 2.87168i) q^{84} +(0.375417 - 0.142377i) q^{85} +(8.59080 + 5.92980i) q^{86} +(0.706187 - 0.174059i) q^{87} +(0.894061 + 0.792069i) q^{88} -16.3418i q^{89} +(-0.189169 + 0.167589i) q^{90} +(7.56531 + 13.9513i) q^{91} +(-1.10201 - 0.976296i) q^{92} +(5.57790 - 6.29615i) q^{93} +(3.23775 + 8.53724i) q^{94} +(0.0732732 - 0.603459i) q^{95} +(-7.28180 + 2.76162i) q^{96} +(9.70057 - 1.17786i) q^{97} +(19.9566 - 13.7750i) q^{98} +3.80516i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.83220	−	0.694863i	−1.29556	−	0.491343i	−0.392067	−	0.919937i	$-0.628240\pi$
$2$	−1.83220	−	0.694863i	−1.29556	−	0.491343i	−0.903497	+	0.428594i	$0.859009\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	1.37712	+	1.22002i	0.688558	+	0.610009i
$5$	−0.128032	−	0.0155459i	−0.0572578	−	0.00695235i	0.0918577	−	0.995772i	$-0.470720\pi$
$5$	−0.128032	−	0.0155459i	−0.0572578	−	0.00695235i	−0.149115	+	0.988820i	$0.547643\pi$
$6$	−0.468949	−	1.90260i	−0.191448	−	0.776734i
$7$	−2.04557	−	3.89750i	−0.773151	−	1.47312i	−0.878016	−	0.478631i	$-0.841133\pi$
$7$	−2.04557	−	3.89750i	−0.773151	−	1.47312i	0.104865	−	0.994486i	$-0.466559\pi$
$8$	0.145878	+	0.277948i	0.0515758	+	0.0982694i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	0.223779	+	0.117448i	0.0707651	+	0.0371404i
$11$	3.55789	−	1.34933i	1.07274	−	0.406838i	0.245914	−	0.969292i	$-0.420912\pi$
$11$	3.55789	−	1.34933i	1.07274	−	0.406838i	0.826829	+	0.562454i	$0.190143\pi$
$12$	−0.221764	+	1.82639i	−0.0640178	+	0.527234i
$13$	−3.60522	+	0.0489021i	−0.999908	+	0.0135630i
$13$	−3.60522	+	0.0489021i	−0.999908	+	0.0135630i
$14$	1.03966	+	8.56241i	0.277862	+	2.28840i
$15$	−0.0599366	−	0.114200i	−0.0154756	−	0.0294862i
$16$	−0.517672	−	4.26341i	−0.129418	−	1.06585i
$17$	−2.75654	+	1.44675i	−0.668560	+	0.350887i	−0.764614	−	0.644489i	$-0.777070\pi$
$17$	−2.75654	+	1.44675i	−0.668560	+	0.350887i	0.0960537	+	0.995376i	$0.469378\pi$
$18$	1.29942	−	1.46674i	0.306276	−	0.345714i
$19$			4.71334i			1.08131i	0.841243	+	0.540657i	$0.181824\pi$
$19$			4.71334i			1.08131i	−0.841243	+	0.540657i	$0.818176\pi$
$20$	−0.157349	−	0.177610i	−0.0351843	−	0.0397148i
$21$	2.04557	−	3.89750i	0.446379	−	0.850505i
$22$	−7.45637			−1.58970
$23$	−0.800231			−0.166860			−0.0834298	−	0.996514i	$-0.526587\pi$
$23$	−0.800231			−0.166860			−0.0834298	+	0.996514i	$0.526587\pi$
$24$	−0.145878	+	0.277948i	−0.0297773	+	0.0567359i
$25$	−4.83856	−	1.19260i	−0.967712	−	0.238520i
$26$	6.63948	+	2.41554i	1.30211	+	0.473726i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	1.93804	−	7.86294i	0.366255	−	1.48596i
$29$	0.257912	−	0.680057i	0.0478930	−	0.126283i	−0.908935	−	0.416937i	$-0.863104\pi$
$29$	0.257912	−	0.680057i	0.0478930	−	0.126283i	0.956828	+	0.290654i	$0.0938727\pi$
$30$	0.0304629	+	0.250885i	0.00556174	+	0.0458051i
$31$	−2.01302	−	8.16715i	−0.361549	−	1.46686i	−0.817018	−	0.576612i	$-0.804375\pi$
$31$	−2.01302	−	8.16715i	−0.361549	−	1.46686i	0.455469	−	0.890252i	$-0.349472\pi$
$32$	−1.86376	+	7.56158i	−0.329470	+	1.33671i
$33$	3.13158	+	2.16158i	0.545139	+	0.376282i
$34$	6.05584	−	0.735312i	1.03857	−	0.126105i
$35$	0.201308	+	0.530806i	0.0340273	+	0.0897226i
$36$	−1.62907	+	0.855001i	−0.271511	+	0.142500i
$37$	−2.53811	−	10.2975i	−0.417262	−	1.69290i	−0.684289	−	0.729211i	$-0.739887\pi$
$37$	−2.53811	−	10.2975i	−0.417262	−	1.69290i	0.267026	−	0.963689i	$-0.413959\pi$
$38$	3.27513	−	8.63580i	0.531296	−	1.40091i
$39$	−2.08824	−	2.93926i	−0.334387	−	0.470658i
$40$	−0.0143562	−	0.0378541i	−0.00226991	−	0.00598526i
$41$	4.40336	−	3.03942i	0.687690	−	0.474678i	−0.172263	−	0.985051i	$-0.555108\pi$
$41$	4.40336	−	3.03942i	0.687690	−	0.474678i	0.859953	+	0.510373i	$0.170493\pi$
$42$	−6.45613	+	5.71963i	−0.996202	+	0.882558i
$43$	−5.17226	−	1.27485i	−0.788763	−	0.194413i	−0.175697	−	0.984444i	$-0.556218\pi$
$43$	−5.17226	−	1.27485i	−0.788763	−	0.194413i	−0.613066	+	0.790032i	$0.710064\pi$
$44$	6.54582	+	2.48250i	0.986820	+	0.374252i
$45$	0.0599366	−	0.114200i	0.00893481	−	0.0170239i
$46$	1.46619	+	0.556051i	0.216177	+	0.0819853i
$47$	−3.08985	−	3.48772i	−0.450701	−	0.508736i	0.478614	−	0.878026i	$-0.341140\pi$
$47$	−3.08985	−	3.48772i	−0.450701	−	0.508736i	−0.929314	+	0.369290i	$0.879601\pi$
$48$	3.21465	−	2.84793i	0.463994	−	0.411063i
$49$	−7.02972	+	10.1843i	−1.00425	+	1.45490i
$50$	8.03654	+	5.54722i	1.13654	+	0.784495i
$51$	−2.75654	−	1.44675i	−0.385993	−	0.202585i
$52$	−5.02447	−	4.33109i	−0.696768	−	0.600614i
$53$	−11.8834	+	6.23691i	−1.63231	+	0.856705i	−0.635930	+	0.771747i	$0.719383\pi$
$53$	−11.8834	+	6.23691i	−1.63231	+	0.856705i	−0.996385	+	0.0849582i	$0.972924\pi$
$54$	1.94526	+	0.236197i	0.264716	+	0.0321423i
$55$	−0.476501	+	0.117447i	−0.0642513	+	0.0158365i
$56$	0.784899	−	1.13712i	0.104886	−	0.151954i
$57$	−3.87900	+	2.67748i	−0.513786	+	0.354641i
$58$	−0.945094	+	1.06679i	−0.124097	+	0.140076i
$59$	−6.37878	−	0.774524i	−0.830446	−	0.100834i	−0.305737	−	0.952116i	$-0.598903\pi$
$59$	−6.37878	−	0.774524i	−0.830446	−	0.100834i	−0.524709	+	0.851282i	$0.675826\pi$
$60$	0.0567860	−	0.230390i	0.00733104	−	0.0297432i
$61$	−6.29223	−	3.30242i	−0.805638	−	0.422831i	0.0110302	−	0.999939i	$-0.496489\pi$
$61$	−6.29223	−	3.30242i	−0.805638	−	0.422831i	−0.816668	+	0.577108i	$0.804181\pi$
$62$	−1.98679	+	16.3627i	−0.252322	+	2.07806i
$63$	4.36959	−	0.530565i	0.550517	−	0.0668449i
$64$	3.78970	−	5.49033i	0.473713	−	0.686291i
$65$	0.462345	+	0.0497854i	0.0573468	+	0.00617512i
$66$	−4.23570	−	6.13647i	−0.521379	−	0.755348i
$67$	8.80563	+	9.93951i	1.07578	+	1.21430i	0.975651	+	0.219330i	$0.0703870\pi$
$67$	8.80563	+	9.93951i	1.07578	+	1.21430i	0.100129	+	0.994974i	$0.468075\pi$
$68$	−5.56114	−	1.37070i	−0.674387	−	0.166221i
$69$	−0.454583	−	0.658577i	−0.0547254	−	0.0792834i
$70$		−	1.11243i		−	0.132960i
$71$	−3.77565	+	2.60615i	−0.448088	+	0.309293i	−0.770653	−	0.637254i	$-0.780070\pi$
$71$	−3.77565	+	2.60615i	−0.448088	+	0.309293i	0.322566	+	0.946547i	$0.395455\pi$
$72$	−0.311615	+	0.0378369i	−0.0367242	+	0.00445912i
$73$	−0.0826716	+	0.0313532i	−0.00967598	+	0.00366962i	−0.359438	−	0.933169i	$-0.617032\pi$
$73$	−0.0826716	+	0.0313532i	−0.00967598	+	0.00366962i	0.349762	+	0.936839i	$0.386262\pi$
$74$	−2.50503	+	20.6308i	−0.291204	+	2.39828i
$75$	−1.76713	−	4.65953i	−0.204050	−	0.538036i
$76$	−5.75036	+	6.49081i	−0.659611	+	0.744547i
$77$	−12.5369	−	11.1067i	−1.42871	−	1.26573i
$78$	1.78371	+	6.83637i	0.201965	+	0.774066i
$79$	6.96403	−	6.16959i	0.783514	−	0.694133i	−0.173288	−	0.984871i	$-0.555439\pi$
$79$	6.96403	−	6.16959i	0.783514	−	0.694133i	0.956803	+	0.290738i	$0.0939008\pi$
$80$			0.553902i			0.0619281i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−10.1798	+	2.50911i	−1.12418	+	0.277084i
$83$	−2.47482	−	1.70825i	−0.271647	−	0.187504i	0.424452	−	0.905451i	$-0.360467\pi$
$83$	−2.47482	−	1.70825i	−0.271647	−	0.187504i	−0.696098	+	0.717946i	$0.745082\pi$
$84$	7.57200	−	2.87168i	0.826173	−	0.313326i
$85$	0.375417	−	0.142377i	0.0407197	−	0.0154430i
$86$	8.59080	+	5.92980i	0.926370	+	0.639427i
$87$	0.706187	−	0.174059i	0.0757112	−	0.0186611i
$88$	0.894061	+	0.792069i	0.0953072	+	0.0844349i
$89$		−	16.3418i		−	1.73223i	−0.499848	−	0.866113i	$-0.666611\pi$
$89$		−	16.3418i		−	1.73223i	0.499848	−	0.866113i	$-0.333389\pi$
$90$	−0.189169	+	0.167589i	−0.0199402	+	0.0176655i
$91$	7.56531	+	13.9513i	0.793060	+	1.46250i
$92$	−1.10201	−	0.976296i	−0.114893	−	0.101786i
$93$	5.57790	−	6.29615i	0.578402	−	0.652881i
$94$	3.23775	+	8.53724i	0.333948	+	0.880549i
$95$	0.0732732	−	0.603459i	0.00751767	−	0.0619136i
$96$	−7.28180	+	2.76162i	−0.743196	+	0.281857i
$97$	9.70057	−	1.17786i	0.984944	−	0.119594i	0.387813	−	0.921738i	$-0.373231\pi$
$97$	9.70057	−	1.17786i	0.984944	−	0.119594i	0.597130	+	0.802144i	$0.296307\pi$
$98$	19.9566	−	13.7750i	2.01592	−	1.39149i
$99$			3.80516i			0.382433i
$100$	−5.20826	−	7.54547i	−0.520826	−	0.754547i
$101$	10.8616	+	2.67714i	1.08077	+	0.266385i	0.739210	−	0.673475i	$-0.235199\pi$
$101$	10.8616	+	2.67714i	1.08077	+	0.266385i	0.341558	+	0.939861i	$0.389045\pi$
$102$	4.04526	+	4.56616i	0.400541	+	0.452117i
$103$	−1.48690	−	2.15414i	−0.146508	−	0.212254i	0.742858	−	0.669449i	$-0.233470\pi$
$103$	−1.48690	−	2.15414i	−0.146508	−	0.212254i	−0.889367	+	0.457195i	$0.848854\pi$
$104$	−0.539516	−	0.994930i	−0.0529039	−	0.0975609i
$105$	−0.322489	+	0.467206i	−0.0314717	+	0.0455946i
$106$	26.1067	−	3.16992i	2.53570	−	0.307890i
$107$	−1.49347	+	12.2998i	−0.144379	+	1.18907i	0.722795	+	0.691063i	$0.242857\pi$
$107$	−1.49347	+	12.2998i	−0.144379	+	1.18907i	−0.867174	+	0.498005i	$0.834066\pi$
$108$	−1.62907	−	0.855001i	−0.156757	−	0.0822725i
$109$	−1.65017	+	6.69500i	−0.158057	+	0.641264i	0.837444	+	0.546523i	$0.184049\pi$
$109$	−1.65017	+	6.69500i	−0.158057	+	0.641264i	−0.995502	+	0.0947418i	$0.969797\pi$
$110$	0.954656	+	0.115916i	0.0910229	+	0.0110522i
$111$	7.03288	−	7.93848i	0.667531	−	0.753487i
$112$	−15.5577	+	10.7387i	−1.47007	+	1.01471i
$113$	6.05932	−	8.77844i	0.570013	−	0.825806i	−0.426902	−	0.904298i	$-0.640395\pi$
$113$	6.05932	−	8.77844i	0.570013	−	0.825806i	0.996915	+	0.0784919i	$0.0250105\pi$
$114$	8.96761	−	2.21032i	0.839893	−	0.207015i
$115$	0.102455	+	0.0124403i	0.00955401	+	0.00116007i
$116$	1.18486	−	0.621861i	0.110011	−	0.0577383i
$117$	1.23270	−	3.38828i	0.113964	−	0.313247i
$118$	11.1490	+	5.85147i	1.02635	+	0.538671i
$119$	11.2774	+	7.78422i	1.03380	+	0.713578i
$120$	0.0229981	−	0.0333185i	0.00209943	−	0.00304155i
$121$	2.60424	−	2.30716i	0.236749	−	0.209742i
$122$	9.23392	+	10.4229i	0.836000	+	0.943649i
$123$	5.00279	+	1.89731i	0.451086	+	0.171075i
$124$	7.19191	−	13.7030i	0.645852	−	1.23057i
$125$	1.20391	+	0.456582i	0.107681	+	0.0408380i
$126$	−8.37466	−	2.06417i	−0.746074	−	0.183891i
$127$	10.1089	−	8.95569i	0.897019	−	0.794689i	−0.0823850	−	0.996601i	$-0.526254\pi$
$127$	10.1089	−	8.95569i	0.897019	−	0.794689i	0.979404	+	0.201911i	$0.0647153\pi$
$128$	2.06007	−	1.42197i	0.182086	−	0.125685i
$129$	−1.88900	−	4.98089i	−0.166317	−	0.438543i
$130$	−0.812516	−	0.412483i	−0.0712623	−	0.0361772i
$131$	−6.97508	+	18.3918i	−0.609416	+	1.60690i	0.173544	+	0.984826i	$0.444478\pi$
$131$	−6.97508	+	18.3918i	−0.609416	+	1.60690i	−0.782960	+	0.622072i	$0.786291\pi$
$132$	1.67539	+	6.79733i	0.145824	+	0.591632i
$133$	18.3702	−	9.64145i	1.59290	−	0.836020i
$134$	−9.22712	−	24.3299i	−0.797102	−	2.10179i
$135$	0.128032	−	0.0155459i	0.0110193	−	0.00133798i
$136$	−0.804240	−	0.555127i	−0.0689630	−	0.0476017i
$137$	3.15684	−	12.8078i	0.269707	−	1.09424i	−0.667260	−	0.744825i	$-0.732533\pi$
$137$	3.15684	−	12.8078i	0.269707	−	1.09424i	0.936967	−	0.349419i	$-0.113621\pi$
$138$	0.375268	+	1.52252i	0.0319449	+	0.129606i
$139$	−1.69395	−	13.9509i	−0.143679	−	1.18330i	−0.868972	−	0.494862i	$-0.835219\pi$
$139$	−1.69395	−	13.9509i	−0.143679	−	1.18330i	0.725293	−	0.688440i	$-0.241704\pi$
$140$	−0.370368	+	0.976581i	−0.0313018	+	0.0825362i
$141$	1.11510	−	4.52415i	0.0939085	−	0.381002i
$142$	8.72869	−	2.15143i	0.732495	−	0.180544i
$143$	−12.7610	+	5.03861i	−1.06713	+	0.421350i
$144$	4.16993	+	1.02779i	0.347494	+	0.0856495i
$145$	−0.0435931	+	0.0830598i	−0.00362021	+	0.00689774i
$146$	0.173257			0.0143389
$147$	−12.3749			−1.02066
$148$	9.06788	−	17.2774i	0.745375	−	1.42019i
$149$	8.38688	+	9.46683i	0.687080	+	0.775553i	0.983773	−	0.179420i	$-0.0574221\pi$
$149$	8.38688	+	9.46683i	0.687080	+	0.775553i	−0.296692	+	0.954973i	$0.595884\pi$
$150$			9.76512i			0.797319i
$151$	−5.86269	+	6.61761i	−0.477099	+	0.538534i	−0.936950	−	0.349462i	$-0.886364\pi$
$151$	−5.86269	+	6.61761i	−0.477099	+	0.538534i	0.459851	+	0.887996i	$0.347903\pi$
$152$	−1.31006	+	0.687574i	−0.106260	+	0.0557696i
$153$	−0.375247	−	3.09044i	−0.0303369	−	0.249847i
$154$	15.2525	+	29.0612i	1.22908	+	2.34182i
$155$	0.130766	+	1.07695i	0.0105034	+	0.0865029i
$156$	0.710195	−	6.59539i	0.0568611	−	0.528054i
$157$	−0.136128	+	1.12111i	−0.0108642	+	0.0894745i	−0.997132	−	0.0756770i	$-0.975888\pi$
$157$	−0.136128	+	1.12111i	−0.0108642	+	0.0894745i	0.986268	+	0.165151i	$0.0528113\pi$
$158$	−17.0465	+	6.46490i	−1.35615	+	0.514320i
$159$	−11.8834	−	6.23691i	−0.942417	−	0.494619i
$160$	0.356174	−	0.939153i	0.0281580	−	0.0742465i
$161$	1.63693	+	3.11890i	0.129008	+	0.245804i
$162$	0.910645	+	1.73509i	0.0715470	+	0.136321i
$163$	1.22168	+	4.95653i	0.0956890	+	0.388226i	0.999185	−	0.0403715i	$-0.0128541\pi$
$163$	1.22168	+	4.95653i	0.0956890	+	0.388226i	−0.903496	+	0.428597i	$0.859008\pi$
$164$	9.77209	+	1.18655i	0.763072	+	0.0926537i
$165$	−0.367340	−	0.325435i	−0.0285974	−	0.0253351i
$166$	3.34738	+	4.84952i	0.259807	+	0.376396i
$167$	−12.9887	−	4.92597i	−1.00510	−	0.381183i	−0.203518	−	0.979071i	$-0.565237\pi$
$167$	−12.9887	−	4.92597i	−1.00510	−	0.381183i	−0.801579	+	0.597888i	$0.796007\pi$
$168$	1.38171			0.106601
$169$	12.9952	−	0.352606i	0.999632	−	0.0271235i
$170$	−0.786774			−0.0603428
$171$	−4.40705	−	1.67137i	−0.337015	−	0.127813i
$172$	−5.56747	−	8.06587i	−0.424515	−	0.615017i
$173$	14.7349	+	13.0540i	1.12027	+	0.992475i	1.00000		0.000265844i	$-8.46209e-5\pi$
$173$	14.7349	+	13.0540i	1.12027	+	0.992475i	0.120273	+	0.992741i	$0.461623\pi$
$174$	−1.41483	−	0.171791i	−0.107258	−	0.0130234i
$175$	5.24944	+	21.2978i	0.396821	+	1.60996i
$176$	−7.59455	−	14.4702i	−0.572461	−	1.09073i
$177$	−2.98614	−	5.68961i	−0.224452	−	0.427657i
$178$	−11.3553	+	29.9415i	−0.851117	+	2.24421i
$179$	15.7742	+	8.27896i	1.17902	+	0.618798i	0.936267	−	0.351289i	$-0.114257\pi$
$179$	15.7742	+	8.27896i	1.17902	+	0.618798i	0.242755	+	0.970088i	$0.421949\pi$
$180$	0.221865	−	0.0841423i	0.0165368	−	0.00627160i
$181$	−0.278051	+	2.28995i	−0.0206673	+	0.170211i	−0.999388	−	0.0349875i	$-0.988861\pi$
$181$	−0.278051	+	2.28995i	−0.0206673	+	0.170211i	0.978720	+	0.205198i	$0.0657839\pi$
$182$	−4.16694	−	30.8185i	−0.308874	−	2.28442i
$183$	−0.856558	−	7.05439i	−0.0633186	−	0.521476i
$184$	−0.116736	−	0.222423i	−0.00860592	−	0.0163972i
$185$	0.164875	+	1.35787i	0.0121219	+	0.0998326i
$186$	−14.5948	+	7.65996i	−1.07014	+	0.561655i
$187$	−7.85533	+	8.86684i	−0.574439	+	0.648407i
$188$		−	8.57267i		−	0.625226i
$189$	2.91886	+	3.29471i	0.212316	+	0.239655i
$190$	−0.553573	+	1.05475i	−0.0401604	+	0.0765193i
$191$	4.80054			0.347355			0.173678	−	0.984803i	$-0.444435\pi$
$191$	4.80054			0.347355			0.173678	+	0.984803i	$0.444435\pi$
$192$	6.67125			0.481456
$193$	−6.77173	+	12.9024i	−0.487440	+	0.928738i	0.510199	+	0.860056i	$0.329572\pi$
$193$	−6.77173	+	12.9024i	−0.487440	+	0.928738i	−0.997639	+	0.0686821i	$0.978121\pi$
$194$	−18.5919	−	4.58249i	−1.33482	−	0.329003i
$195$	0.221669	+	0.408783i	0.0158740	+	0.0292736i
$196$	−22.1058	+	5.44859i	−1.57898	+	0.389185i
$197$	0.716266	−	2.90600i	0.0510318	−	0.207044i	−0.939891	−	0.341474i	$-0.889074\pi$
$197$	0.716266	−	2.90600i	0.0510318	−	0.207044i	0.990923	+	0.134429i	$0.0429202\pi$
$198$	2.64407	−	6.97183i	0.187906	−	0.495466i
$199$	−1.49883	−	12.3440i	−0.106249	−	0.875042i	−0.944217	−	0.329323i	$-0.893180\pi$
$199$	−1.49883	−	12.3440i	−0.106249	−	0.875042i	0.837968	−	0.545719i	$-0.183743\pi$
$200$	−0.374361	−	1.51884i	−0.0264713	−	0.107398i
$201$	−3.17788	+	12.8932i	−0.224151	+	0.909415i
$202$	−18.0404	−	12.4524i	−1.26932	−	0.876146i
$203$	−3.17810	+	0.385891i	−0.223059	+	0.0270843i
$204$	−2.03102	−	5.35537i	−0.142200	−	0.374951i
$205$	−0.611023	+	0.320690i	−0.0426757	+	0.0223979i
$206$	1.22746	+	4.98002i	0.0855215	+	0.346974i
$207$	0.283766	−	0.748229i	0.0197231	−	0.0520055i
$208$	2.07481	+	15.3452i	0.143862	+	1.06400i
$209$	6.35984	+	16.7695i	0.439919	+	1.15997i
$210$	0.915509	−	0.631930i	0.0631761	−	0.0436073i
$211$	4.22859	−	3.74620i	0.291108	−	0.257899i	−0.504910	−	0.863172i	$-0.668474\pi$
$211$	4.22859	−	3.74620i	0.291108	−	0.257899i	0.796018	+	0.605273i	$0.206936\pi$
$212$	−23.9740	−	5.90906i	−1.64654	−	0.405836i
$213$	−4.28963	−	1.62684i	−0.293921	−	0.111469i
$214$	11.2830	−	21.4980i	0.771292	−	1.46957i
$215$	0.642398	+	0.243629i	0.0438112	+	0.0166154i
$216$	−0.208157	−	0.234960i	−0.0141633	−	0.0159870i
$217$	−27.7137	+	24.5522i	−1.88133	+	1.66671i
$218$	7.67555	−	11.1200i	0.519854	−	0.753139i
$219$	−0.0727660	−	0.0502268i	−0.00491707	−	0.00339401i
$220$	−0.799484	−	0.419601i	−0.0539012	−	0.0282895i
$221$	9.86720	−	5.35064i	0.663740	−	0.359923i
$222$	−18.4018	+	9.65802i	−1.23505	+	0.648204i
$223$	−12.1409	−	1.47417i	−0.813016	−	0.0987180i	−0.296541	−	0.955020i	$-0.595833\pi$
$223$	−12.1409	−	1.47417i	−0.813016	−	0.0987180i	−0.516475	+	0.856302i	$0.672756\pi$
$224$	33.2837	−	8.20370i	2.22386	−	0.548133i
$225$	2.83087	−	4.10123i	0.188725	−	0.273415i
$226$	−17.2017	+	11.8735i	−1.14424	+	0.789813i
$227$	−5.66608	+	6.39568i	−0.376071	+	0.424496i	−0.905823	−	0.423656i	$-0.860746\pi$
$227$	−5.66608	+	6.39568i	−0.376071	+	0.424496i	0.529752	+	0.848153i	$0.322285\pi$
$228$	−8.60841	−	1.04525i	−0.570106	−	0.0692234i
$229$	6.36466	−	25.8225i	0.420589	−	1.70640i	−0.253150	−	0.967427i	$-0.581467\pi$
$229$	6.36466	−	25.8225i	0.420589	−	1.70640i	0.673739	−	0.738969i	$-0.264687\pi$
$230$	−0.179075	−	0.0939857i	−0.0118078	−	0.00619723i
$231$	2.01888	−	16.6270i	0.132833	−	1.09398i
$232$	0.226644	−	0.0275196i	0.0148799	−	0.00180675i
$233$	16.4478	−	23.8287i	1.07753	−	1.56107i	0.277865	−	0.960620i	$-0.410373\pi$
$233$	16.4478	−	23.8287i	1.07753	−	1.56107i	0.799663	−	0.600449i	$-0.205012\pi$
$234$	−4.61296	+	5.35146i	−0.301558	+	0.349836i
$235$	0.341381	+	0.494575i	0.0222692	+	0.0322625i
$236$	−7.83938	−	8.84883i	−0.510300	−	0.576010i
$237$	9.03349	+	2.22656i	0.586788	+	0.144630i
$238$	−15.2535	−	22.0985i	−0.988738	−	1.43243i
$239$		−	1.87587i		−	0.121340i	−0.998158	−	0.0606698i	$-0.980676\pi$
$239$		−	1.87587i		−	0.121340i	0.998158	−	0.0606698i	$-0.0193237\pi$
$240$	−0.455852	+	0.314652i	−0.0294251	+	0.0203107i
$241$	12.8602	−	1.56151i	0.828398	−	0.100586i	0.304656	−	0.952462i	$-0.401459\pi$
$241$	12.8602	−	1.56151i	0.828398	−	0.100586i	0.523742	+	0.851877i	$0.324535\pi$
$242$	−6.37466	+	2.41759i	−0.409779	+	0.155409i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	−4.63612	−	12.2244i	−0.296797	−	0.782590i
$245$	1.05836	−	1.19464i	0.0676159	−	0.0763225i
$246$	−7.84776	−	6.95251i	−0.500355	−	0.443276i
$247$	−0.230492	−	16.9926i	−0.0146659	−	1.08121i
$248$	1.97639	−	1.75092i	0.125501	−	0.111184i
$249$		−	3.00713i		−	0.190569i
$250$	−1.88854	−	1.67310i	−0.119442	−	0.105816i
$251$	−7.71505	+	1.90159i	−0.486970	+	0.120027i	−0.475153	−	0.879903i	$-0.657607\pi$
$251$	−7.71505	+	1.90159i	−0.486970	+	0.120027i	−0.0118162	+	0.999930i	$0.503761\pi$
$252$	6.66474	+	4.60034i	0.419839	+	0.289794i
$253$	−2.84713	+	1.07977i	−0.178997	+	0.0678848i
$254$	−24.7445	+	9.38436i	−1.55261	+	0.588827i
$255$	0.330435	+	0.228083i	0.0206927	+	0.0142831i
$256$	−17.7173	+	4.36693i	−1.10733	+	0.272933i
$257$	−16.4376	−	14.5624i	−1.02535	−	0.908380i	−0.0295155	−	0.999564i	$-0.509396\pi$
$257$	−16.4376	−	14.5624i	−1.02535	−	0.908380i	−0.995834	+	0.0911839i	$0.970935\pi$
$258$			10.4386i			0.649879i
$259$	−34.9427	+	30.9565i	−2.17123	+	1.92355i
$260$	0.575963	+	0.632629i	0.0357197	+	0.0392340i
$261$	0.544408	+	0.482303i	0.0336980	+	0.0298538i
$262$	25.5596	−	28.8508i	1.57907	−	1.78241i
$263$	7.81588	+	20.6088i	0.481948	+	1.27079i	0.926924	+	0.375250i	$0.122443\pi$
$263$	7.81588	+	20.6088i	0.481948	+	1.27079i	−0.444976	+	0.895543i	$0.646788\pi$
$264$	−0.143975	+	1.18574i	−0.00886108	+	0.0729775i
$265$	1.61842	−	0.613786i	0.0994188	−	0.0377046i
$266$	−40.3575	+	4.90029i	−2.47448	+	0.300456i
$267$	13.4490	−	9.28320i	0.823067	−	0.568122i
$268$			24.4309i			1.49235i
$269$	0.513045	+	0.743274i	0.0312809	+	0.0453182i	0.838312	−	0.545190i	$-0.183543\pi$
$269$	0.513045	+	0.743274i	0.0312809	+	0.0453182i	−0.807031	+	0.590508i	$0.798927\pi$
$270$	−0.245384	−	0.0604816i	−0.0149336	−	0.00368079i
$271$	14.5971	+	16.4767i	0.886709	+	1.00089i	0.999973	+	0.00732277i	$0.00233093\pi$
$271$	14.5971	+	16.4767i	0.886709	+	1.00089i	−0.113264	+	0.993565i	$0.536131\pi$
$272$	7.59506	+	11.0033i	0.460518	+	0.667175i
$273$	−7.18412	+	14.1514i	−0.434803	+	0.856481i
$274$	−14.6836	+	21.2729i	−0.887071	+	1.28514i
$275$	−18.8242	+	2.28568i	−1.13514	+	0.137831i
$276$	0.177463	−	1.46154i	0.0106820	−	0.0879742i
$277$	−8.54560	−	4.48508i	−0.513456	−	0.269482i	0.188033	−	0.982163i	$-0.439789\pi$
$277$	−8.54560	−	4.48508i	−0.513456	−	0.269482i	−0.701489	+	0.712680i	$0.747481\pi$
$278$	−6.59033	+	26.7380i	−0.395262	+	1.60364i
$279$	8.35024	+	1.01390i	0.499916	+	0.0607008i
$280$	−0.118170	+	0.133386i	−0.00706200	+	0.00797136i
$281$	−5.80984	+	4.01024i	−0.346586	+	0.239231i	−0.728621	−	0.684917i	$-0.759839\pi$
$281$	−5.80984	+	4.01024i	−0.346586	+	0.239231i	0.382036	+	0.924148i	$0.375223\pi$
$282$	−5.18676	+	7.51432i	−0.308867	+	0.447471i
$283$	0.321000	−	0.0791193i	0.0190814	−	0.00470315i	−0.229763	−	0.973247i	$-0.573795\pi$
$283$	0.321000	−	0.0791193i	0.0190814	−	0.00470315i	0.248845	+	0.968543i	$0.419949\pi$
$284$	−8.37906	−	1.01740i	−0.497206	−	0.0603717i
$285$	0.538261	−	0.282501i	0.0318838	−	0.0167339i
$286$	26.8819	−	0.364632i	1.58956	−	0.0215611i
$287$	−20.8535	−	10.9448i	−1.23094	−	0.646050i
$288$	−6.40930	−	4.42402i	−0.377672	−	0.260688i
$289$	−4.15164	+	6.01469i	−0.244214	+	0.353805i
$290$	0.137587	−	0.121891i	0.00807937	−	0.00715770i
$291$	6.47991	+	7.31431i	0.379859	+	0.428773i
$292$	−0.152100	−	0.0576839i	−0.00890097	−	0.00337569i
$293$	9.43856	−	17.9837i	0.551407	−	1.05062i	−0.437096	−	0.899415i	$-0.643993\pi$
$293$	9.43856	−	17.9837i	0.551407	−	1.05062i	0.988503	−	0.151203i	$-0.0483147\pi$
$294$	22.6733	+	8.59884i	1.32233	+	0.501494i
$295$	0.804649	+	0.198328i	0.0468485	+	0.0115471i
$296$	2.49192	−	2.20765i	0.144840	−	0.128317i
$297$	−3.13158	+	2.16158i	−0.181713	+	0.125427i
$298$	−8.78832	−	23.1729i	−0.509094	−	1.34237i
$299$	2.88501	−	0.0391330i	0.166844	−	0.00226312i
$300$	3.25117	−	8.57264i	0.187706	−	0.494941i
$301$	5.61149	+	22.7667i	0.323441	+	1.31225i
$302$	15.3400	−	8.05105i	0.882717	−	0.463286i
$303$	3.96684	+	10.4597i	0.227889	+	0.600894i
$304$	20.0949	−	2.43996i	1.15252	−	0.139941i
$305$	0.754269	+	0.520635i	0.0431893	+	0.0298114i
$306$	−1.45990	+	5.92306i	−0.0834571	+	0.338599i
$307$	−6.77448	−	27.4851i	−0.386640	−	1.56866i	−0.765644	−	0.643265i	$-0.777580\pi$
$307$	−6.77448	−	27.4851i	−0.386640	−	1.56866i	0.379004	−	0.925395i	$-0.376267\pi$
$308$	−3.71436	−	30.5905i	−0.211645	−	1.74305i
$309$	0.928170	−	2.44738i	0.0528018	−	0.139227i
$310$	0.508745	−	2.06406i	0.0288948	−	0.117231i
$311$	−9.27062	+	2.28500i	−0.525688	+	0.129571i	−0.493224	−	0.869902i	$-0.664182\pi$
$311$	−9.27062	+	2.28500i	−0.525688	+	0.129571i	−0.0324644	+	0.999473i	$0.510336\pi$
$312$	0.512331	−	1.00920i	0.0290050	−	0.0571345i
$313$	4.07207	+	1.00368i	0.230167	+	0.0567311i	0.352712	−	0.935732i	$-0.385259\pi$
$313$	4.07207	+	1.00368i	0.230167	+	0.0567311i	−0.122545	+	0.992463i	$0.539106\pi$
$314$	1.02843	−	1.95952i	0.0580379	−	0.110582i
$315$	−0.567697			−0.0319861
$316$	17.1173			0.962922
$317$	0.476861	−	0.908583i	0.0267832	−	0.0510311i	−0.871697	−	0.490046i	$-0.836980\pi$
$317$	0.476861	−	0.908583i	0.0267832	−	0.0510311i	0.898480	+	0.439015i	$0.144672\pi$
$318$	17.4391	+	19.6846i	0.977935	+	1.10386i
$319$		−	2.76757i		−	0.154954i
$320$	−0.570556	+	0.644025i	−0.0318951	+	0.0360021i
$321$	−10.9709	+	5.75799i	−0.612338	+	0.321380i
$322$	−0.831972	−	6.85190i	−0.0463640	−	0.381842i
$323$	−6.81900	−	12.9925i	−0.379420	−	0.722923i
$324$	−0.221764	−	1.82639i	−0.0123202	−	0.101466i
$325$	17.5024	+	4.06296i	0.970858	+	0.225372i
$326$	1.20575	−	9.93028i	0.0667806	−	0.549987i
$327$	−6.44728	+	2.44513i	−0.356535	+	0.135216i
$328$	1.48716	+	0.780520i	0.0821145	+	0.0430970i
$329$	−7.27290	+	19.1771i	−0.400968	+	1.05727i
$330$	0.446909	+	0.851514i	0.0246015	+	0.0468743i
$331$	−13.7977	−	26.2893i	−0.758390	−	1.44499i	−0.891086	−	0.453834i	$-0.850056\pi$
$331$	−13.7977	−	26.2893i	−0.758390	−	1.44499i	0.132697	−	0.991157i	$-0.457636\pi$
$332$	−1.32402	−	5.37178i	−0.0726653	−	0.294815i
$333$	10.5284	+	1.27838i	0.576951	+	0.0700545i
$334$	20.3751	+	18.0508i	1.11488	+	0.987694i
$335$	−0.972886	−	1.40947i	−0.0531545	−	0.0770075i
$336$	−17.6756	−	6.70346i	−0.964282	−	0.365704i
$337$	14.9449			0.814101			0.407051	−	0.913406i	$-0.366557\pi$
$337$	14.9449			0.814101			0.407051	+	0.913406i	$0.366557\pi$
$338$	−24.0549	−	8.38386i	−1.30841	−	0.456022i
$339$	10.6666			0.579330
$340$	0.690696	+	0.261946i	0.0374582	+	0.0142060i
$341$	−18.1823	−	26.3415i	−0.984624	−	1.42647i
$342$	6.91324	+	6.12459i	0.373825	+	0.331180i
$343$	23.4860	+	2.85171i	1.26812	+	0.153978i
$344$	−0.400180	−	1.62359i	−0.0215762	−	0.0875383i
$345$	0.0479631	+	0.0913860i	0.00258225	+	0.00492006i
$346$	−17.9266	−	34.1563i	−0.963740	−	1.83625i
$347$	−12.5903	+	33.1980i	−0.675885	+	1.78216i	−0.0546933	+	0.998503i	$0.517418\pi$
$347$	−12.5903	+	33.1980i	−0.675885	+	1.78216i	−0.621192	+	0.783659i	$0.713351\pi$
$348$	1.18486	+	0.621861i	0.0635150	+	0.0333352i
$349$	−1.20724	+	0.457846i	−0.0646221	+	0.0245079i	−0.386704	−	0.922204i	$-0.626387\pi$
$349$	−1.20724	+	0.457846i	−0.0646221	+	0.0245079i	0.322082	+	0.946712i	$0.395617\pi$
$350$	5.18103	−	42.6696i	0.276938	−	2.28079i
$351$	3.48876	−	0.910267i	0.186216	−	0.0485864i
$352$	3.57200	+	29.4181i	0.190388	+	1.56799i
$353$	−8.85014	−	16.8625i	−0.471046	−	0.897502i	−0.998841	−	0.0481308i	$-0.984674\pi$
$353$	−8.85014	−	16.8625i	−0.471046	−	0.897502i	0.527795	−	0.849371i	$-0.323019\pi$
$354$	1.51771	+	12.4995i	0.0806655	+	0.664340i
$355$	0.523920	−	0.274975i	0.0278068	−	0.0145941i
$356$	19.9373	−	22.5045i	1.05667	−	1.19274i
$357$			13.7030i			0.725242i
$358$	−23.1489	−	26.1297i	−1.22346	−	1.38100i
$359$	−6.39758	+	12.1896i	−0.337651	+	0.643341i	−0.993787	−	0.111303i	$-0.964498\pi$
$359$	−6.39758	+	12.1896i	−0.337651	+	0.643341i	0.656135	+	0.754643i	$0.272190\pi$
$360$	0.0404850			0.00213375
$361$	−3.21556			−0.169240
$362$	2.10065	−	4.00245i	0.110408	−	0.210364i
$363$	3.37813	+	0.832635i	0.177306	+	0.0437020i
$364$	−6.60255	+	28.4424i	−0.346068	+	1.49079i
$365$	0.0110720	−	0.00272901i	0.000579537	−	0.000142843i
$366$	−3.33245	+	13.5203i	−0.174190	+	0.706716i
$367$	−4.43118	+	11.6841i	−0.231306	+	0.609904i	−0.999542	−	0.0302631i	$-0.990365\pi$
$367$	−4.43118	+	11.6841i	−0.231306	+	0.609904i	0.768236	+	0.640167i	$0.221135\pi$
$368$	0.414257	+	3.41171i	0.0215946	+	0.177848i
$369$	1.28045	+	5.19501i	0.0666578	+	0.270441i
$370$	0.641449	−	2.60246i	0.0333474	−	0.135296i
$371$	48.6167	+	33.5577i	2.52405	+	1.74223i
$372$	15.3628	−	1.86539i	0.796526	−	0.0967158i
$373$	−7.01859	−	18.5065i	−0.363409	−	0.958230i	−0.984639	−	0.174602i	$-0.944136\pi$
$373$	−7.01859	−	18.5065i	−0.363409	−	0.958230i	0.621230	−	0.783628i	$-0.286633\pi$
$374$	20.5538	−	10.7875i	1.06281	−	0.557807i
$375$	0.308138	+	1.25017i	0.0159122	+	0.0645583i
$376$	0.518662	−	1.36760i	0.0267480	−	0.0705286i
$377$	−0.896572	+	2.46437i	−0.0461758	+	0.126921i
$378$	−3.05857	−	8.06479i	−0.157316	−	0.414808i
$379$	22.5911	−	15.5935i	1.16043	−	0.800985i	0.177345	−	0.984149i	$-0.443249\pi$
$379$	22.5911	−	15.5935i	1.16043	−	0.800985i	0.983083	+	0.183163i	$0.0586337\pi$
$380$	0.837137	−	0.741639i	0.0429442	−	0.0380453i
$381$	13.1129	+	3.23204i	0.671794	+	0.165582i
$382$	−8.79558	−	3.33572i	−0.450021	−	0.170670i
$383$	−2.14001	+	4.07745i	−0.109349	+	0.208348i	−0.933981	−	0.357322i	$-0.883690\pi$
$383$	−2.14001	+	4.07745i	−0.109349	+	0.208348i	0.824632	+	0.565670i	$0.191382\pi$
$384$	2.34051	+	0.887638i	0.119439	+	0.0452971i
$385$	1.43246	+	1.61692i	0.0730051	+	0.0824057i
$386$	21.3726	−	18.9345i	1.08784	−	0.963740i
$387$	3.02611	−	4.38408i	0.153826	−	0.222855i
$388$	14.7958	+	10.2128i	0.751144	+	0.518477i
$389$	19.0867	+	10.0175i	0.967733	+	0.507906i	0.873065	−	0.487603i	$-0.162129\pi$
$389$	19.0867	+	10.0175i	0.967733	+	0.507906i	0.0946679	+	0.995509i	$0.469821\pi$
$390$	−0.122094	−	0.903005i	−0.00618248	−	0.0457254i
$391$	2.20587	−	1.15773i	0.111556	−	0.0585490i
$392$	−3.85619	−	0.468226i	−0.194767	−	0.0236490i
$393$	−19.0984	+	4.70734i	−0.963389	+	0.237454i
$394$	−3.33162	+	4.82669i	−0.167845	+	0.243165i
$395$	−0.987532	+	0.681644i	−0.0496881	+	0.0342972i
$396$	−4.64236	+	5.24014i	−0.233287	+	0.263327i
$397$	−1.07264	−	0.130242i	−0.0538344	−	0.00653668i	0.0935752	−	0.995612i	$-0.470170\pi$
$397$	−1.07264	−	0.130242i	−0.0538344	−	0.00653668i	−0.147410	+	0.989076i	$0.547094\pi$
$398$	−5.83122	+	23.6582i	−0.292293	+	1.18588i
$399$	18.3702	+	9.64145i	0.919663	+	0.482676i
$400$	−2.57975	+	21.2461i	−0.128987	+	1.06231i
$401$	2.59395	−	0.314963i	0.129536	−	0.0157285i	−0.0555119	−	0.998458i	$-0.517679\pi$
$401$	2.59395	−	0.314963i	0.129536	−	0.0157285i	0.185048	+	0.982730i	$0.440756\pi$
$402$	14.7815	−	21.4147i	0.737236	−	1.06807i
$403$	7.65677	+	29.3459i	0.381411	+	1.46182i
$404$	11.6915	+	16.9381i	0.581674	+	0.842700i
$405$	0.0855246	+	0.0965374i	0.00424975	+	0.00479698i
$406$	6.09107	+	1.50131i	0.302295	+	0.0745090i
$407$	−22.9250	−	33.2126i	−1.13635	−	1.64629i
$408$		−	0.977225i		−	0.0483798i
$409$	−15.5818	+	10.7553i	−0.770469	+	0.531817i	−0.887221	−	0.461345i	$-0.847367\pi$
$409$	−15.5818	+	10.7553i	−0.770469	+	0.531817i	0.116752	+	0.993161i	$0.462752\pi$
$410$	1.34235	−	0.162991i	0.0662942	−	0.00804957i
$411$	12.3339	−	4.67763i	0.608386	−	0.230730i
$412$	0.580463	−	4.78054i	0.0285974	−	0.235520i
$413$	10.0295	+	26.4456i	0.493520	+	1.30130i
$414$	−1.03983	+	1.17373i	−0.0511050	+	0.0576857i
$415$	0.290301	+	0.257184i	0.0142503	+	0.0126247i
$416$	6.34950	−	27.3523i	0.311310	−	1.34106i
$417$	10.5191	−	9.31912i	0.515123	−	0.456359i
$418$		−	35.1444i		−	1.71897i
$419$	15.7165	+	13.9236i	0.767801	+	0.680212i	0.953163	−	0.302458i	$-0.0978073\pi$
$419$	15.7165	+	13.9236i	0.767801	+	0.680212i	−0.185362	+	0.982670i	$0.559346\pi$
$420$	−1.01410	+	0.249954i	−0.0494832	+	0.0121965i
$421$	−2.86794	−	1.97960i	−0.139775	−	0.0964797i	0.496125	−	0.868251i	$-0.334756\pi$
$421$	−2.86794	−	1.97960i	−0.139775	−	0.0964797i	−0.635900	+	0.771771i	$0.719371\pi$
$422$	−10.3507	+	3.92552i	−0.503866	+	0.191091i
$423$	4.35675	−	1.65230i	0.211832	−	0.0803374i
$424$	−3.46707	−	2.39315i	−0.168376	−	0.116221i
$425$	15.0631	−	3.71272i	0.730667	−	0.180093i
$426$	6.72905	+	5.96142i	0.326023	+	0.288832i
$427$			31.2793i			1.51371i
$428$	−17.0627	+	15.1162i	−0.824756	+	0.730670i
$429$	−11.3958	−	7.63982i	−0.550192	−	0.368854i
$430$	−1.00771	−	0.892758i	−0.0485963	−	0.0430526i
$431$	9.77906	−	11.0383i	0.471041	−	0.531695i	−0.464189	−	0.885736i	$-0.653654\pi$
$431$	9.77906	−	11.0383i	0.471041	−	0.531695i	0.935230	+	0.354041i	$0.115193\pi$
$432$	1.52293	+	4.01564i	0.0732720	+	0.193202i
$433$	4.05917	−	33.4303i	0.195071	−	1.60656i	−0.485744	−	0.874101i	$-0.661451\pi$
$433$	4.05917	−	33.4303i	0.195071	−	1.60656i	0.680816	−	0.732455i	$-0.261626\pi$
$434$	67.8376	−	25.7274i	3.25631	−	1.23495i
$435$	−0.0931206	+	0.0113069i	−0.00446479	+	0.000542124i
$436$	−10.4405	+	7.20655i	−0.500009	+	0.345131i
$437$		−	3.77176i		−	0.180428i
$438$	0.0984215	+	0.142588i	0.00470276	+	0.00681312i
$439$	2.51251	+	0.619279i	0.119916	+	0.0295566i	0.298817	−	0.954311i	$-0.403408\pi$
$439$	2.51251	+	0.619279i	0.119916	+	0.0295566i	−0.178901	+	0.983867i	$0.557254\pi$
$440$	−0.102155	−	0.115309i	−0.00487006	−	0.00549716i
$441$	−7.02972	−	10.1843i	−0.334749	−	0.484967i
$442$	−21.7967	+	2.94711i	−1.03676	+	0.140180i
$443$	8.07345	−	11.6964i	0.383581	−	0.555713i	−0.582869	−	0.812566i	$-0.698070\pi$
$443$	8.07345	−	11.6964i	0.383581	−	0.555713i	0.966451	+	0.256853i	$0.0826855\pi$
$444$	19.3702	−	2.35196i	0.919268	−	0.111619i
$445$	−0.254048	+	2.09228i	−0.0120430	+	0.0991834i
$446$	21.2203	+	11.1373i	1.00481	+	0.527365i
$447$	−3.02676	+	12.2800i	−0.143161	+	0.580826i
$448$	−29.1507	−	3.53953i	−1.37724	−	0.167227i
$449$	−5.31026	+	5.99404i	−0.250607	+	0.282876i	−0.860330	−	0.509738i	$-0.829742\pi$
$449$	−5.31026	+	5.99404i	−0.250607	+	0.282876i	0.609723	+	0.792615i	$0.291281\pi$
$450$	−8.03654	+	5.54722i	−0.378846	+	0.261498i
$451$	11.5655	−	16.7555i	0.544597	−	0.788985i
$452$	19.0542	−	4.69645i	0.896236	−	0.220902i
$453$	−8.77658	−	1.06567i	−0.412360	−	0.0500695i
$454$	14.8255	−	7.78105i	0.695797	−	0.365183i
$455$	−0.751718	−	1.90383i	−0.0352411	−	0.0892528i
$456$	−1.31006	−	0.687574i	−0.0613493	−	0.0321986i
$457$	−1.38659	−	0.957095i	−0.0648620	−	0.0447710i	0.535192	−	0.844730i	$-0.320239\pi$
$457$	−1.38659	−	0.957095i	−0.0648620	−	0.0447710i	−0.600055	+	0.799959i	$0.704854\pi$
$458$	−29.6044	+	42.8894i	−1.38332	+	2.00409i
$459$	2.33021	−	2.06439i	0.108765	−	0.0963575i
$460$	0.125915	+	0.142129i	0.00587084	+	0.00662681i
$461$	−6.42182	−	2.43547i	−0.299094	−	0.113431i	0.200493	−	0.979695i	$-0.435746\pi$
$461$	−6.42182	−	2.43547i	−0.299094	−	0.113431i	−0.499587	+	0.866264i	$0.666515\pi$
$462$	−15.2525	+	29.0612i	−0.709611	+	1.35205i
$463$	29.1399	+	11.0513i	1.35424	+	0.513597i	0.921661	−	0.387997i	$-0.126833\pi$
$463$	29.1399	+	11.0513i	1.35424	+	0.513597i	0.432584	+	0.901594i	$0.357602\pi$
$464$	−3.03288	−	0.747537i	−0.140798	−	0.0347035i
$465$	−0.812031	+	0.719397i	−0.0376570	+	0.0333612i
$466$	−46.6933	+	32.2301i	−2.16303	+	1.49303i
$467$	5.51803	+	14.5498i	0.255344	+	0.673286i	0.999983	+	0.00581911i	$0.00185229\pi$
$467$	5.51803	+	14.5498i	0.255344	+	0.673286i	−0.744639	+	0.667467i	$0.767378\pi$
$468$	5.83134	−	3.16213i	0.269554	−	0.146170i
$469$	20.7267	−	54.6519i	0.957071	−	2.52359i
$470$	−0.281817	−	1.14338i	−0.0129992	−	0.0527400i
$471$	−0.999987	+	0.524834i	−0.0460770	+	0.0241831i
$472$	−0.715248	−	1.88595i	−0.0329220	−	0.0868081i
$473$	−20.1225	+	2.44332i	−0.925234	+	0.112344i
$474$	−15.0040	−	10.3565i	−0.689159	−	0.475692i
$475$	5.62112	−	22.8058i	0.257915	−	1.04640i
$476$	6.03338	+	24.4784i	0.276540	+	1.12197i
$477$	−1.61769	−	13.3228i	−0.0740687	−	0.610011i
$478$	−1.30347	+	3.43697i	−0.0596194	+	0.157203i
$479$	0.594948	−	2.41380i	0.0271839	−	0.110289i	−0.955783	−	0.294074i	$-0.904989\pi$
$479$	0.594948	−	2.41380i	0.0271839	−	0.110289i	0.982967	+	0.183785i	$0.0588349\pi$
$480$	0.975237	−	0.240374i	0.0445133	−	0.0109715i
$481$	9.65401	+	37.0007i	0.440185	+	1.68709i
$482$	−24.6475	−	6.07508i	−1.12267	−	0.276712i
$483$	−1.63693	+	3.11890i	−0.0744827	+	0.141915i
$484$	6.40112			0.290960
$485$	−1.26030			−0.0572271
$486$	−0.910645	+	1.73509i	−0.0413077	+	0.0787052i
$487$	−11.9174	−	13.4520i	−0.540030	−	0.609568i	0.413633	−	0.910444i	$-0.364260\pi$
$487$	−11.9174	−	13.4520i	−0.540030	−	0.609568i	−0.953663	+	0.300876i	$0.902721\pi$
$488$		−	2.23066i		−	0.100977i
$489$	−3.38516	+	3.82105i	−0.153082	+	0.172794i
$490$	−2.76923	+	1.45341i	−0.125101	+	0.0656582i
$491$	2.37629	+	19.5705i	0.107240	+	0.883204i	0.942698	+	0.333648i	$0.108280\pi$
$491$	2.37629	+	19.5705i	0.107240	+	0.883204i	−0.835457	+	0.549555i	$0.814797\pi$
$492$	4.57467	+	8.71631i	0.206242	+	0.392962i
$493$	0.272925	+	2.24774i	0.0122919	+	0.101233i
$494$	−11.3852	+	31.2941i	−0.512246	+	1.40799i
$495$	0.0591547	−	0.487183i	0.00265881	−	0.0218972i
$496$	−33.7778	+	12.8102i	−1.51667	+	0.575197i
$497$	17.8808	+	9.38457i	0.802064	+	0.420956i
$498$	−2.08955	+	5.50968i	−0.0936348	+	0.246895i
$499$	−13.8339	−	26.3582i	−0.619288	−	1.17996i	−0.969916	−	0.243441i	$-0.921724\pi$
$499$	−13.8339	−	26.3582i	−0.619288	−	1.17996i	0.350627	−	0.936515i	$-0.385968\pi$
$500$	1.10088	+	2.09756i	0.0492330	+	0.0938056i
$501$	−3.32444	−	13.4878i	−0.148525	−	0.602589i
$502$	15.4569	+	1.87681i	0.689875	+	0.0837660i
$503$	−32.9709	−	29.2097i	−1.47010	−	1.30239i	−0.860245	−	0.509882i	$-0.829689\pi$
$503$	−32.9709	−	29.2097i	−1.47010	−	1.30239i	−0.609855	−	0.792513i	$-0.708772\pi$
$504$	0.784899	+	1.13712i	0.0349622	+	0.0506514i
$505$	−1.34901	−	0.511613i	−0.0600303	−	0.0227665i
$506$	5.96682			0.265257
$507$	7.67231	+	10.4946i	0.340739	+	0.466079i
$508$	24.8472			1.10242
$509$	−28.2809	−	10.7255i	−1.25353	−	0.475401i	−0.363625	−	0.931546i	$-0.618461\pi$
$509$	−28.2809	−	10.7255i	−1.25353	−	0.475401i	−0.889906	+	0.456144i	$0.849230\pi$
$510$	−0.446939	−	0.647502i	−0.0197908	−	0.0286719i
$511$	0.291309	+	0.258078i	0.0128868	+	0.0114167i
$512$	30.5263	+	3.70657i	1.34909	+	0.163809i
$513$	−1.12798	−	4.57638i	−0.0498014	−	0.202052i
$514$	19.9981	+	38.1033i	0.882080	+	1.68066i
$515$	0.156883	+	0.298915i	0.00691307	+	0.0131718i
$516$	3.47540	−	9.16387i	0.152996	−	0.403417i
$517$	−15.6994	−	8.23968i	−0.690459	−	0.362381i
$518$	85.5327	−	32.4383i	3.75809	−	1.42526i
$519$	−2.37284	+	19.5421i	−0.104156	+	0.857802i
$520$	0.0536083	+	0.135770i	0.00235088	+	0.00595392i
$521$	−2.05617	−	16.9341i	−0.0900823	−	0.741895i	−0.965839	−	0.259142i	$-0.916560\pi$
$521$	−2.05617	−	16.9341i	−0.0900823	−	0.741895i	0.875757	−	0.482752i	$-0.160363\pi$
$522$	−0.662332	−	1.26197i	−0.0289895	−	0.0552348i
$523$	3.07428	+	25.3190i	0.134429	+	1.10712i	0.891254	+	0.453505i	$0.149827\pi$
$523$	3.07428	+	25.3190i	0.134429	+	1.10712i	−0.756825	+	0.653618i	$0.773250\pi$
$524$	−32.0438	+	16.8179i	−1.39984	+	0.734693i
$525$	−14.5457	+	16.4188i	−0.634828	+	0.716573i
$526$		−	43.1905i		−	1.88319i
$527$	17.3648	+	19.6008i	0.756421	+	0.853823i
$528$	7.59455	−	14.4702i	0.330511	−	0.629735i
$529$	−22.3596			−0.972158
$530$	−3.39177			−0.147329
$531$	2.98614	−	5.68961i	0.129587	−	0.246908i
$532$	37.0607	+	9.13464i	1.60678	+	0.396037i
$533$	−15.7265	+	11.1731i	−0.681188	+	0.483961i
$534$	−31.0919	+	7.66347i	−1.34548	+	0.331631i
$535$	0.382424	−	1.55156i	0.0165336	−	0.0670796i
$536$	−1.47811	+	3.89747i	−0.0638448	+	0.168345i
$537$	2.14734	+	17.6849i	0.0926645	+	0.763161i
$538$	−0.423529	−	1.71833i	−0.0182596	−	0.0740823i
$539$	−11.2690	+	45.7200i	−0.485389	+	1.96930i
$540$	0.195282	+	0.134793i	0.00840358	+	0.00580057i
$541$	13.5699	−	1.64768i	0.583415	−	0.0708394i	0.176492	−	0.984302i	$-0.443525\pi$
$541$	13.5699	−	1.64768i	0.583415	−	0.0708394i	0.406923	+	0.913463i	$0.366602\pi$
$542$	−15.2958	−	40.3316i	−0.657010	−	1.73239i
$543$	−2.04254	+	1.07201i	−0.0876540	+	0.0460044i
$544$	−5.80215	−	23.5402i	−0.248765	−	1.00928i
$545$	0.315355	−	0.831522i	0.0135083	−	0.0356185i
$546$	22.9961	−	20.9362i	0.984140	−	0.895988i
$547$	−2.97826	−	7.85303i	−0.127341	−	0.335771i	0.856150	−	0.516728i	$-0.172850\pi$
$547$	−2.97826	−	7.85303i	−0.127341	−	0.335771i	−0.983491	+	0.180956i	$0.942081\pi$
$548$	19.9731	−	13.7864i	0.853207	−	0.588926i
$549$	5.31907	−	4.71229i	0.227012	−	0.201115i
$550$	36.0781	+	8.89245i	1.53837	+	0.379175i
$551$	3.20534	+	1.21563i	0.136552	+	0.0517874i
$552$	0.116736	−	0.222423i	0.00496863	−	0.00946693i
$553$	−38.2914	−	14.5220i	−1.62831	−	0.617538i
$554$	12.5408	+	14.1556i	0.532806	+	0.601414i
$555$	−1.02385	+	0.907048i	−0.0434598	+	0.0385021i
$556$	14.6876	−	21.2787i	0.622894	−	0.902417i
$557$	7.96981	+	5.50116i	0.337692	+	0.233092i	0.724827	−	0.688931i	$-0.241920\pi$
$557$	7.96981	+	5.50116i	0.337692	+	0.233092i	−0.387135	+	0.922023i	$0.626535\pi$
$558$	−14.5948	−	7.65996i	−0.617848	−	0.324272i
$559$	18.7095	+	4.34317i	0.791327	+	0.183697i
$560$	2.15883	−	1.13304i	0.0912273	−	0.0478798i
$561$	−11.7596	−	1.42787i	−0.496491	−	0.0602849i
$562$	13.4314	−	3.31054i	0.566568	−	0.139647i
$563$	−13.4202	+	19.4426i	−0.565596	+	0.819407i	−0.996552	−	0.0829656i	$-0.973561\pi$
$563$	−13.4202	+	19.4426i	−0.565596	+	0.819407i	0.430957	+	0.902373i	$0.358176\pi$
$564$	7.05517	−	4.86983i	0.297076	−	0.205057i
$565$	−0.912257	+	1.02973i	−0.0383789	+	0.0433209i
$566$	−0.643114	−	0.0780882i	−0.0270321	−	0.00328229i
$567$	−1.05339	+	4.27378i	−0.0442383	+	0.179482i
$568$	−1.27516	−	0.669255i	−0.0535045	−	0.0280813i
$569$	3.82512	−	31.5027i	0.160357	−	1.32066i	−0.661060	−	0.750333i	$-0.729893\pi$
$569$	3.82512	−	31.5027i	0.160357	−	1.32066i	0.821417	−	0.570328i	$-0.193184\pi$
$570$	−1.18250	+	0.143582i	−0.0495297	+	0.00601399i
$571$	−13.1167	+	19.0028i	−0.548917	+	0.795244i	−0.995013	−	0.0997409i	$-0.968199\pi$
$571$	−13.1167	+	19.0028i	−0.548917	+	0.795244i	0.446096	+	0.894985i	$0.352814\pi$
$572$	−23.7205	−	8.62987i	−0.991805	−	0.360833i
$573$	2.72702	+	3.95077i	0.113923	+	0.165046i
$574$	30.6028	+	34.5434i	1.27734	+	1.44181i
$575$	3.87196	+	0.954353i	0.161472	+	0.0397993i
$576$	3.78970	+	5.49033i	0.157904	+	0.228764i
$577$		−	27.8456i		−	1.15923i	−0.814891	−	0.579614i	$-0.803203\pi$
$577$		−	27.8456i		−	1.15923i	0.814891	−	0.579614i	$-0.196797\pi$
$578$	11.7860	−	8.13532i	0.490235	−	0.338385i
$579$	−14.4653	+	1.75640i	−0.601157	+	0.0729936i
$580$	−0.161367	+	0.0611985i	−0.00670041	+	0.00254113i
$581$	−1.59548	+	13.1400i	−0.0661916	+	0.545137i
$582$	−6.79008	−	17.9040i	−0.281458	−	0.742143i
$583$	−33.8642	+	38.2248i	−1.40251	+	1.58311i
$584$	−0.0207746	−	0.0184047i	−0.000859657	−	0.000761590i
$585$	−0.210500	+	0.414646i	−0.00870310	+	0.0171435i
$586$	−29.7896	+	26.3913i	−1.23060	+	1.09021i
$587$		−	21.6591i		−	0.893965i	−0.894543	−	0.446982i	$-0.852499\pi$
$587$		−	21.6591i		−	0.893965i	0.894543	−	0.446982i	$-0.147501\pi$
$588$	−17.0416	−	15.0976i	−0.702784	−	0.622613i
$589$	38.4945	−	9.48805i	1.58614	−	0.390948i
$590$	−1.33647	−	0.922498i	−0.0550216	−	0.0379787i
$591$	2.79848	−	1.06132i	0.115114	−	0.0436570i
$592$	−42.5886	+	16.1517i	−1.75038	+	0.663832i
$593$	−17.9743	−	12.4068i	−0.738118	−	0.509486i	0.138685	−	0.990337i	$-0.455713\pi$
$593$	−17.9743	−	12.4068i	−0.738118	−	0.509486i	−0.876803	+	0.480851i	$0.840328\pi$
$594$	7.23970	−	1.78443i	0.297049	−	0.0732159i
$595$	−1.32286	−	1.17195i	−0.0542318	−	0.0480452i
$596$			23.2691i			0.953138i
$597$	9.30746	−	8.24569i	0.380929	−	0.337474i
$598$	−5.31312	−	1.93299i	−0.217269	−	0.0790457i
$599$	2.45395	+	2.17401i	0.100266	+	0.0888277i	0.711767	−	0.702416i	$-0.247895\pi$
$599$	2.45395	+	2.17401i	0.100266	+	0.0888277i	−0.611501	+	0.791244i	$0.709434\pi$
$600$	1.03732	−	1.17089i	0.0423484	−	0.0478015i
$601$	−8.68575	−	22.9024i	−0.354299	−	0.934210i	−0.987130	−	0.159920i	$-0.948876\pi$
$601$	−8.68575	−	22.9024i	−0.354299	−	0.934210i	0.632831	−	0.774290i	$-0.281893\pi$
$602$	5.53835	−	45.6125i	0.225726	−	1.85902i
$603$	−12.4161	+	4.70881i	−0.505624	+	0.191758i
$604$	−16.1472	+	1.96063i	−0.657021	+	0.0797768i
$605$	−0.369294	+	0.254905i	−0.0150139	+	0.0103634i
$606$		−	21.9207i		−	0.890468i
$607$	−11.8741	−	17.2026i	−0.481956	−	0.698234i	0.504287	−	0.863536i	$-0.331755\pi$
$607$	−11.8741	−	17.2026i	−0.481956	−	0.698234i	−0.986243	+	0.165303i	$0.947140\pi$
$608$	−35.6403	−	8.78455i	−1.44541	−	0.356260i
$609$	−2.12295	−	2.39631i	−0.0860262	−	0.0971035i
$610$	−1.02021	−	1.47802i	−0.0413069	−	0.0598434i
$611$	11.3101	+	12.4229i	0.457559	+	0.502576i
$612$	3.25363	−	4.71370i	0.131520	−	0.190540i
$613$	−21.3526	+	2.59267i	−0.862422	+	0.104717i	−0.539782	−	0.841805i	$-0.681493\pi$
$613$	−21.3526	+	2.59267i	−0.862422	+	0.104717i	−0.322640	+	0.946522i	$0.604570\pi$
$614$	−6.68619	+	55.0657i	−0.269833	+	2.22227i
$615$	−0.611023	−	0.320690i	−0.0246388	−	0.0129315i
$616$	1.25823	−	5.10483i	0.0506955	−	0.205680i
$617$	41.0721	+	4.98705i	1.65350	+	0.200771i	0.893472	−	0.449119i	$-0.148262\pi$
$617$	41.0721	+	4.98705i	1.65350	+	0.200771i	0.760028	+	0.649890i	$0.225185\pi$
$618$	−3.40119	+	3.83916i	−0.136816	+	0.154433i
$619$	−23.4750	+	16.2037i	−0.943542	+	0.651280i	−0.937234	−	0.348700i	$-0.886623\pi$
$619$	−23.4750	+	16.2037i	−0.943542	+	0.651280i	−0.00630754	+	0.999980i	$0.502008\pi$
$620$	−1.13382	+	1.64262i	−0.0455354	+	0.0659694i
$621$	0.776978	−	0.191508i	0.0311790	−	0.00768494i
$622$	18.5734	+	2.25522i	0.744727	+	0.0904262i
$623$	−63.6922	+	33.4282i	−2.55177	+	1.33927i
$624$	−11.4502	+	10.4246i	−0.458376	+	0.417318i
$625$	21.9157	+	11.5023i	0.876629	+	0.460090i
$626$	−6.76345	−	4.66848i	−0.270322	−	0.186590i
$627$	−10.1882	+	14.7602i	−0.406879	+	0.589466i
$628$	−1.55524	+	1.37782i	−0.0620609	+	0.0549811i
$629$	21.8943	+	24.7135i	0.872983	+	0.985394i
$630$	1.04014	+	0.394472i	0.0414401	+	0.0157161i
$631$	−15.7472	+	30.0038i	−0.626886	+	1.19443i	0.340289	+	0.940321i	$0.389475\pi$
$631$	−15.7472	+	30.0038i	−0.626886	+	1.19443i	−0.967175	+	0.254111i	$0.918217\pi$
$632$	2.73073	+	1.03563i	0.108622	+	0.0411951i
$633$	5.48518	+	1.35198i	0.218016	+	0.0537362i
$634$	−1.50505	+	1.33336i	−0.0597731	+	0.0529543i
$635$	−1.43349	+	0.989465i	−0.0568862	+	0.0392657i
$636$	−8.75572	−	23.0869i	−0.347187	−	0.915457i
$637$	24.8457	−	37.0604i	0.984421	−	1.46839i
$638$	−1.92309	+	5.07076i	−0.0761357	+	0.200753i
$639$	−1.09792	−	4.45445i	−0.0434332	−	0.176215i
$640$	−0.285861	+	0.150032i	−0.0112997	+	0.00593052i
$641$	−0.308162	−	0.812556i	−0.0121717	−	0.0320940i	0.928793	−	0.370600i	$-0.120848\pi$
$641$	−0.308162	−	0.812556i	−0.0121717	−	0.0320940i	−0.940964	+	0.338506i	$0.890079\pi$
$642$	24.1020	−	2.92651i	0.951231	−	0.115500i
$643$	18.8089	+	12.9829i	0.741751	+	0.511994i	0.877988	−	0.478683i	$-0.158886\pi$
$643$	18.8089	+	12.9829i	0.741751	+	0.511994i	−0.136237	+	0.990676i	$0.543501\pi$
$644$	−1.55088	+	6.29217i	−0.0611132	+	0.247946i
$645$	0.164421	+	0.667080i	0.00647405	+	0.0262663i
$646$	3.46578	+	28.5432i	0.136359	+	1.12302i
$647$	8.05686	−	21.2442i	0.316748	−	0.835196i	−0.678207	−	0.734871i	$-0.737243\pi$
$647$	8.05686	−	21.2442i	0.316748	−	0.835196i	0.994955	−	0.100325i	$-0.0319881\pi$
$648$	0.0751221	−	0.304782i	0.00295107	−	0.0119730i
$649$	−23.7400	+	5.85140i	−0.931878	+	0.229687i
$650$	−29.2447	−	19.6059i	−1.14707	−	0.769008i
$651$	−35.9492	−	8.86069i	−1.40896	−	0.347278i
$652$	−4.36467	+	8.31619i	−0.170934	+	0.325687i
$653$	0.417010			0.0163189			0.00815943	−	0.999967i	$-0.497403\pi$
$653$	0.417010			0.0163189			0.00815943	+	0.999967i	$0.497403\pi$
$654$	13.5118			0.528352
$655$	1.17895	−	2.24631i	0.0460655	−	0.0877705i
$656$	−15.2378	−	17.1999i	−0.594936	−	0.671544i
$657$		−	0.0884173i		−	0.00344949i
$658$	26.6509	−	30.0826i	1.03896	−	1.17274i
$659$	23.7216	−	12.4501i	0.924064	−	0.484986i	0.0655917	−	0.997847i	$-0.479107\pi$
$659$	23.7216	−	12.4501i	0.924064	−	0.484986i	0.858472	+	0.512861i	$0.171414\pi$
$660$	−0.108833	−	0.896323i	−0.00423633	−	0.0348893i
$661$	−19.1817	−	36.5477i	−0.746081	−	1.42154i	−0.901093	−	0.433627i	$-0.857234\pi$
$661$	−19.1817	−	36.5477i	−0.746081	−	1.42154i	0.155011	−	0.987913i	$-0.450459\pi$
$662$	7.01271	+	57.7549i	0.272557	+	2.24471i
$663$	10.0087	+	5.08104i	0.388706	+	0.197331i
$664$	0.113781	−	0.937068i	0.00441554	−	0.0363653i
$665$	−2.50187	+	0.948834i	−0.0970183	+	0.0367942i
$666$	−18.4018	−	9.65802i	−0.713056	−	0.374241i
$667$	−0.206389	+	0.544203i	−0.00799141	+	0.0210716i
$668$	−11.8772	−	22.6301i	−0.459542	−	0.875585i
$669$	−5.68361	−	10.8292i	−0.219741	−	0.418681i
$670$	0.803138	+	3.25846i	0.0310279	+	0.125885i
$671$	−26.8431	−	3.25934i	−1.03627	−	0.125825i
$672$	25.6588	+	22.7317i	0.989811	+	0.876896i
$673$	−4.34255	−	6.29126i	−0.167393	−	0.242510i	0.730306	−	0.683120i	$-0.239378\pi$
$673$	−4.34255	−	6.29126i	−0.167393	−	0.242510i	−0.897699	+	0.440610i	$0.854762\pi$
$674$	−27.3821	−	10.3847i	−1.05472	−	0.400003i
$675$	4.98337			0.191810
$676$	18.3261	+	15.3688i	0.704850	+	0.591109i
$677$	−5.95927			−0.229033			−0.114517	−	0.993421i	$-0.536532\pi$
$677$	−5.95927			−0.229033			−0.114517	+	0.993421i	$0.536532\pi$
$678$	−19.5434	−	7.41183i	−0.750559	−	0.284650i
$679$	−24.4339	−	35.3986i	−0.937686	−	1.35847i
$680$	0.0943387	+	0.0835768i	0.00361772	+	0.00320502i
$681$	−8.48224	−	1.02993i	−0.325040	−	0.0394670i
$682$	15.0098	+	60.8973i	0.574756	+	2.33188i
$683$	−7.05454	−	13.4413i	−0.269934	−	0.514317i	0.712324	−	0.701851i	$-0.247643\pi$
$683$	−7.05454	−	13.4413i	−0.269934	−	0.514317i	−0.982258	+	0.187534i	$0.939951\pi$
$684$	−4.02991	−	7.67835i	−0.154087	−	0.293589i
$685$	−0.603286	+	1.59073i	−0.0230504	+	0.0607788i
$686$	−41.0495	−	21.5445i	−1.56728	−	0.822571i
$687$	24.8670	−	9.43081i	0.948735	−	0.359808i
$688$	−2.75767	+	22.7114i	−0.105135	+	0.865865i
$689$	42.5374	−	23.0665i	1.62055	−	0.878765i
$690$	−0.0243774	−	0.200766i	−0.000928030	−	0.00764302i
$691$	−0.843078	−	1.60635i	−0.0320722	−	0.0611085i	0.868893	−	0.495001i	$-0.164832\pi$
$691$	−0.843078	−	1.60635i	−0.0320722	−	0.0611085i	−0.900965	+	0.433892i	$0.857140\pi$
$692$	4.36556	+	35.9537i	0.165954	+	1.36675i
$693$	14.8306	−	7.78370i	0.563368	−	0.295679i
$694$	46.1362	−	52.0769i	1.75130	−	1.97681i
$695$			1.81250i			0.0687521i
$696$	0.151397	+	0.170892i	0.00573868	+	0.00647763i
$697$	−7.74079	+	14.7488i	−0.293203	+	0.558652i
$698$	2.53005			0.0957639
$699$	28.9540			1.09514
$700$	−18.7546	+	35.7340i	−0.708859	+	1.35062i
$701$	−15.2276	−	3.75328i	−0.575140	−	0.141759i	−0.0589918	−	0.998258i	$-0.518789\pi$
$701$	−15.2276	−	3.75328i	−0.575140	−	0.141759i	−0.516149	+	0.856499i	$0.672635\pi$
$702$	−7.02462	−	0.756414i	−0.265127	−	0.0285490i
$703$	48.5357	−	11.9630i	1.83056	−	0.451192i
$704$	6.07507	−	24.6475i	0.228963	−	0.928938i
$705$	−0.213101	+	0.561901i	−0.00802585	+	0.0211624i
$706$	4.49811	+	37.0453i	0.169289	+	1.39422i
$707$	−11.7839	−	47.8093i	−0.443180	−	1.79805i
$708$	2.82917	−	11.4784i	0.106327	−	0.431385i
$709$	−21.9401	−	15.1442i	−0.823979	−	0.568751i	0.0797709	−	0.996813i	$-0.474581\pi$
$709$	−21.9401	−	15.1442i	−0.823979	−	0.568751i	−0.903749	+	0.428062i	$0.859197\pi$
$710$	−1.15100	+	0.139757i	−0.0431962	+	0.00524497i
$711$	3.29919	+	8.69925i	0.123729	+	0.326247i
$712$	4.54217	−	2.38391i	0.170225	−	0.0893409i
$713$	1.61088	+	6.53560i	0.0603280	+	0.244760i
$714$	9.52175	−	25.1068i	0.356342	−	0.939598i
$715$	1.71215	−	0.446724i	0.0640306	−	0.0167065i
$716$	11.6225	+	30.6459i	0.434352	+	1.14529i
$717$	1.54381	−	1.06561i	0.0576545	−	0.0397961i
$718$	20.1917	−	17.8883i	0.753549	−	0.667587i
$719$	28.8038	+	7.09951i	1.07420	+	0.264767i	0.736467	−	0.676474i	$-0.236493\pi$
$719$	28.8038	+	7.09951i	1.07420	+	0.264767i	0.337736	+	0.941241i	$0.390339\pi$
$720$	−0.517907	−	0.196416i	−0.0193013	−	0.00732000i
$721$	−5.35422	+	10.2016i	−0.199402	+	0.379928i
$722$	5.89157	+	2.23438i	0.219262	+	0.0831549i
$723$	8.59052	+	9.69670i	0.319485	+	0.360624i
$724$	−3.17669	+	2.81430i	−0.118061	+	0.104593i
$725$	−2.05896	+	2.98291i	−0.0764677	+	0.110783i
$726$	−5.61086	−	3.87290i	−0.208239	−	0.143737i
$727$	25.5632	+	13.4166i	0.948086	+	0.497594i	0.866558	−	0.499077i	$-0.166328\pi$
$727$	25.5632	+	13.4166i	0.948086	+	0.497594i	0.0815284	+	0.996671i	$0.474020\pi$
$728$	−2.77412	+	4.13796i	−0.102816	+	0.153363i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	−0.0221825	−	0.00269345i	−0.000821013	−	9.96890e-5i
$731$	16.1020	−	3.96878i	0.595552	−	0.146790i
$732$	7.42691	−	10.7597i	0.274506	−	0.397691i
$733$	−8.99903	+	6.21158i	−0.332387	+	0.229430i	−0.722555	−	0.691314i	$-0.757032\pi$
$733$	−8.99903	+	6.21158i	−0.332387	+	0.229430i	0.390168	+	0.920744i	$0.372417\pi$
$734$	16.2377	−	18.3285i	0.599343	−	0.676519i
$735$	1.58438	+	0.192379i	0.0584408	+	0.00709599i
$736$	1.49144	−	6.05101i	0.0549752	−	0.223043i
$737$	44.7411	+	23.4819i	1.64806	+	0.864968i
$738$	1.26377	−	10.4081i	0.0465199	−	0.383126i
$739$	40.4668	−	4.91355i	1.48859	−	0.180748i	0.664537	−	0.747255i	$-0.268629\pi$
$739$	40.4668	−	4.91355i	1.48859	−	0.180748i	0.824057	+	0.566507i	$0.191706\pi$
$740$	−1.42957	+	2.07110i	−0.0525522	+	0.0761350i
$741$	13.8537	−	9.84260i	0.508929	−	0.361577i
$742$	−65.7577	−	95.2665i	−2.41404	−	3.49734i
$743$	3.74573	+	4.22805i	0.137417	+	0.155112i	0.813191	−	0.581997i	$-0.197729\pi$
$743$	3.74573	+	4.22805i	0.137417	+	0.155112i	−0.675773	+	0.737110i	$0.736190\pi$
$744$	2.56370	+	0.631895i	0.0939897	+	0.0231664i
$745$	−0.926621	−	1.34244i	−0.0339487	−	0.0491833i
$746$			38.7846i			1.42001i
$747$	2.47482	−	1.70825i	0.0905490	−	0.0625015i
$748$	−21.6354	+	2.62701i	−0.791069	+	0.0960531i
$749$	50.9935	−	19.3393i	1.86326	−	0.706642i
$750$	0.304122	−	2.50467i	0.0111050	−	0.0914577i
$751$	12.6484	+	33.3512i	0.461548	+	1.21700i	0.940691	+	0.339265i	$0.110178\pi$
$751$	12.6484	+	33.3512i	0.461548	+	1.21700i	−0.479143	+	0.877737i	$0.659052\pi$
$752$	−13.2700	+	14.9788i	−0.483909	+	0.546220i
$753$	−5.94762	−	5.26914i	−0.216743	−	0.192018i
$754$	3.35510	−	3.89223i	0.122186	−	0.141747i
$755$	0.853491	−	0.756127i	0.0310617	−	0.0275183i
$756$			8.09826i			0.294531i
$757$	0.903827	+	0.800721i	0.0328501	+	0.0291027i	0.679388	−	0.733779i	$-0.262245\pi$
$757$	0.903827	+	0.800721i	0.0328501	+	0.0291027i	−0.646538	+	0.762882i	$0.723784\pi$
$758$	−52.2269	+	12.8728i	−1.89697	+	0.467560i
$759$	−2.50599	−	1.72976i	−0.0909617	−	0.0627863i
$760$	0.178419	−	0.0676655i	0.00647195	−	0.00245449i
$761$	−32.8657	+	12.4643i	−1.19138	+	0.451831i	−0.869016	−	0.494784i	$-0.835247\pi$
$761$	−32.8657	+	12.4643i	−1.19138	+	0.451831i	−0.322365	+	0.946615i	$0.604478\pi$
$762$	−21.7797	−	15.0334i	−0.788994	−	0.544604i
$763$	29.4693	−	7.26353i	1.06686	−	0.262957i
$764$	6.61091	+	5.85675i	0.239174	+	0.211890i
$765$			0.401509i			0.0145166i
$766$	6.75420	−	5.98370i	0.244039	−	0.216200i
$767$	23.0348	+	2.48039i	0.831737	+	0.0895618i
$768$	−13.6585	−	12.1004i	−0.492859	−	0.436635i
$769$	17.2895	−	19.5158i	0.623475	−	0.703758i	−0.348906	−	0.937158i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83220 - 0.694863i) q^{2} +(0.568065 + 0.822984i) q^{3} +(1.37712 + 1.22002i) q^{4} +(-0.128032 - 0.0155459i) q^{5} +(-0.468949 - 1.90260i) q^{6} +(-2.04557 - 3.89750i) q^{7} +(0.145878 + 0.277948i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.223779 + 0.117448i) q^{10} +(3.55789 - 1.34933i) q^{11} +(-0.221764 + 1.82639i) q^{12} +(-3.60522 + 0.0489021i) q^{13} +(1.03966 + 8.56241i) q^{14} +(-0.0599366 - 0.114200i) q^{15} +(-0.517672 - 4.26341i) q^{16} +(-2.75654 + 1.44675i) q^{17} +(1.29942 - 1.46674i) q^{18} +4.71334i q^{19} +(-0.157349 - 0.177610i) q^{20} +(2.04557 - 3.89750i) q^{21} -7.45637 q^{22} -0.800231 q^{23} +(-0.145878 + 0.277948i) q^{24} +(-4.83856 - 1.19260i) q^{25} +(6.63948 + 2.41554i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(1.93804 - 7.86294i) q^{28} +(0.257912 - 0.680057i) q^{29} +(0.0304629 + 0.250885i) q^{30} +(-2.01302 - 8.16715i) q^{31} +(-1.86376 + 7.56158i) q^{32} +(3.13158 + 2.16158i) q^{33} +(6.05584 - 0.735312i) q^{34} +(0.201308 + 0.530806i) q^{35} +(-1.62907 + 0.855001i) q^{36} +(-2.53811 - 10.2975i) q^{37} +(3.27513 - 8.63580i) q^{38} +(-2.08824 - 2.93926i) q^{39} +(-0.0143562 - 0.0378541i) q^{40} +(4.40336 - 3.03942i) q^{41} +(-6.45613 + 5.71963i) q^{42} +(-5.17226 - 1.27485i) q^{43} +(6.54582 + 2.48250i) q^{44} +(0.0599366 - 0.114200i) q^{45} +(1.46619 + 0.556051i) q^{46} +(-3.08985 - 3.48772i) q^{47} +(3.21465 - 2.84793i) q^{48} +(-7.02972 + 10.1843i) q^{49} +(8.03654 + 5.54722i) q^{50} +(-2.75654 - 1.44675i) q^{51} +(-5.02447 - 4.33109i) q^{52} +(-11.8834 + 6.23691i) q^{53} +(1.94526 + 0.236197i) q^{54} +(-0.476501 + 0.117447i) q^{55} +(0.784899 - 1.13712i) q^{56} +(-3.87900 + 2.67748i) q^{57} +(-0.945094 + 1.06679i) q^{58} +(-6.37878 - 0.774524i) q^{59} +(0.0567860 - 0.230390i) q^{60} +(-6.29223 - 3.30242i) q^{61} +(-1.98679 + 16.3627i) q^{62} +(4.36959 - 0.530565i) q^{63} +(3.78970 - 5.49033i) q^{64} +(0.462345 + 0.0497854i) q^{65} +(-4.23570 - 6.13647i) q^{66} +(8.80563 + 9.93951i) q^{67} +(-5.56114 - 1.37070i) q^{68} +(-0.454583 - 0.658577i) q^{69} -1.11243i q^{70} +(-3.77565 + 2.60615i) q^{71} +(-0.311615 + 0.0378369i) q^{72} +(-0.0826716 + 0.0313532i) q^{73} +(-2.50503 + 20.6308i) q^{74} +(-1.76713 - 4.65953i) q^{75} +(-5.75036 + 6.49081i) q^{76} +(-12.5369 - 11.1067i) q^{77} +(1.78371 + 6.83637i) q^{78} +(6.96403 - 6.16959i) q^{79} +0.553902i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-10.1798 + 2.50911i) q^{82} +(-2.47482 - 1.70825i) q^{83} +(7.57200 - 2.87168i) q^{84} +(0.375417 - 0.142377i) q^{85} +(8.59080 + 5.92980i) q^{86} +(0.706187 - 0.174059i) q^{87} +(0.894061 + 0.792069i) q^{88} -16.3418i q^{89} +(-0.189169 + 0.167589i) q^{90} +(7.56531 + 13.9513i) q^{91} +(-1.10201 - 0.976296i) q^{92} +(5.57790 - 6.29615i) q^{93} +(3.23775 + 8.53724i) q^{94} +(0.0732732 - 0.603459i) q^{95} +(-7.28180 + 2.76162i) q^{96} +(9.70057 - 1.17786i) q^{97} +(19.9566 - 13.7750i) q^{98} +3.80516i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

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